Here it is: the return of the hottest big Jaguar. And this XJR is the most powerful yet. The latest incarnation of the luxury super-saloon comes during a purple patch for Jaguar's performance models: the XFR remains one of the best supersaloons around, the F-type is gaining plaudits and the recent XKR-S GT represents more than a simple test bed for new developments.

The XJR's figures are certainly impressive: 542bhp and 502lb ft, which is 39bhp and 42lb ft up on the XJ Supersport with which it shares its engine. The all-aluminium, quad-cam 5.0-litre V8 features the same Rootes-type, twin vortex supercharger as the Supersport, but has specific electronic engine calibration and a new exhaust system. Jaguar claims 0-60mph in 4.4sec, 50-75mph in 2.46sec and a top speed limited to 174mph.

Despite sharing much with the Supersport, the XJR does without the Paul Smith suit-inspired purple glovebox lining. Shame: it's a charismatic feature

Those numbers aren't wildly in excess of the Supersport, but the XJR pulls more strongly from 3000rpm, and where the lesser motor's torque curve plateaus, the R's continues to rise. The result is a marginally more linear power delivery and sharper in-gear acceleration.

Jaguar has tuned the exhaust and intake to be refined at a cruise but emit a rich, deep rumble under load. There's an oddly tappety sound from outside the car as it accelerates, but from the inside you hear a bassline of the old school.

There's plenty of urge on tap, and it makes for a devastatingly effective point-and-squirt overtaker, helped in part by the sharp-shifting eight-speed automatic gearbox from ZF.

The XJR features new steering hydraulics and calibration and is ten per cent more responsive around the dead-ahead. The steering is both consistent and precise and weights up well as steering inputs increase. It also feels weightier than the Supersport, which can at times feel slightly vague. During a session on track, the long-wheelbase XJR, which will go on sale after the standard-wheelbase model, revealed itself to be a surprisingly controllable machine. Plenty of grip is offered by the 265/35 and 295/30 Pirelli P Zero rubber, but when the power finally overcomes the rears, the chassis balance deeply impresses.

Much of the cornering aplomb is added by new spring rates and damper tuning. The XJR is 30 per cent firmer than the standard XJ and 10 per cent stiffer than the Supersport. The software mapping of the electronic differential and stability control is also bespoke to the XJR. In its track settling, the DSC is unusually unobtrusive, offering the vaguest suggestion that it is operating in the background.

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The exterior features new front and rear spoilers and skirts, which Jaguar says have been shaped by aerodynamics software, 100 hours of wind tunnel testing and time on track, although the visual result isn't radically different from Sport pack-equipped XJs. The 20in forged alloy wheels are specific to the XJR and house 380mm and 376mm discs front and rear. Only after prolonged track use was there some sponginess, but they remained able to haul the XJR's considerable 1870kg from 140mph to half that in short order time and time again.

On track, the XJR handles like a car half its size. The adaptive damping uses 13 different parameters to adjust 100 times a second to control roll, pitch, squat and dive to keep the car composed under high forces.

We have reservations about the ride quality, though. The XJR jittered over the odd piece of scarred tarmacadam on our generally smooth test route. If that remains true on UK roads, it'll mean a more regally-riding Supersport is the better bet. And if the slight performance deficit is a problem, tick the Sport pack option. You'll be left with a car that's a few per cent less capable on track, but one that will provide a more pliant real-world ride.

For those seeking the ultimate XJ, the R is a worthy adversary to the Mercedes S63 and Maserati Quattroporte V8 with which it has been designed to compete.

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